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For each integer $n$, let $f(n)$ be the sum of the elements of the $n$th row (i.e. the row with $n+1$ elements) of Pascal's triangle minus the sum of all the elements from previous rows.

 

For example,

$f(2) = \underbrace{(1 + 2 + 1)}_{\text{2nd row}} - \underbrace{(1 + 1 + 1)}_{\text{0th and 1st rows}} = 1.$

 

What is the minimum value of $f(n)$ for $n \ge 2015$?

 Mar 23, 2021
 #1
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I saw the problem here at another post.

 

https://web2.0calc.com/questions/for-each-integer-n-let-f-n-be-the-sum-of-the-elements

 

But, i do not fully understand it. Does it mean, that... minimum f(n) for n >= 2015, will be $2^{2014} + 1$???

 Mar 23, 2021
 #2
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basically, sir cphill said that f(n) for any positive value of n would just be 1, as the difference between the sum of the elements of the nth row, and the sum of all elements from the previous rows, is just one. you can read his post at the link the guest above me gave. :)

 Mar 24, 2021

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